Glasses formed from nano- and microparticles form a fascinating testing ground to explore and understand the origins of vitrification. For atomic and molecular glasses, a wide range of fragilities have been observed; in colloidal systems, these effects can be emulated by adjusting the particle softness. The colloidal glass transition can range from a superexponential, fragile increase in viscosity with increasing density for hard spheres to a strong, Arrhenius-like transition for compressible particles. However, the microscopic origin of fragility and strength remains elusive, both in the colloidal and in the atomic domains. Here, we propose a simple model that explains fragility changes in colloidal glasses by describing the volume regulation of compressible colloids in order to maintain osmotic equilibrium. Our simple model provides a microscopic explanation for fragility, and we show that it can describe experimental data for a variety of soft colloidal systems, ranging from microgels to star polymers and proteins. Our results highlight that the elastic energy per particle acts as an effective fragility order parameter, leading to a universal description of the colloidal glass transition.